Fractal Approach of Structuring by Fragmentation

Suteanu, Cristian; Zugravescu, D.; Munteanu, Florin

doi:10.1007/978-3-0348-8430-3_4

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…(2020) found that the fragment size distribution defined two power‐law trends (two slopes, or D ‐values, in a log‐log plot) that intersect at a value of

s

= ∼10 μm (Figure 4). Such “bifractal” distributions are observed in a wide range of different processes from drilling, brecciation, crushing, and milling of rock (Barnett, 2004; Carpinteri & Pugno, 2002; Farris & Paterson, 2007; Roy et al., 2012; Taşdemir, 2009) to rapid shock fragmentation of brick, glass, quartz, rock and ceramic (Barnett, 2004; Capaccioni et al., 1986; Davydova et al., 2014; Fujiwara et al., 1977; Hossain & Kruhl, 2015; Keulen et al., 2007; Roy et al., 2012; Suteanu et al., 2000). Bifractal distributions are sometimes interpreted as identifying a grinding limit (e.g., Keulen et al., 2007), but 10 μm is far too large for the grinding limit of garnet (∼0.26 μm for almandine‐pyrope; B. R. Song, Johnson, Song, et al., 2020).…”

Section: Calculation Of Fragment Size For Surface Energy and Strain R...mentioning

confidence: 99%

Energy Partitioning, Dynamic Fragmentation, and Off‐Fault Damage in the Earthquake Source Volume

et al. 2021

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During an earthquake, released elastic strain energy rel E U is converted to the energy conv E U required to advance the rupture and to overcome the frictional resistance to slip on the trailing fault (see Table 1 for notation used in this paper). The rest radiates away as elastodynamic waves rad E U that produce ground shaking. rad E U is the only quantity that can be directly measured and generally comprises less than 15%-20% of rel E U (e.g., Lachenbruch &

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“…(2020) found that the fragment size distribution defined two power‐law trends (two slopes, or D ‐values, in a log‐log plot) that intersect at a value of

s

Section: Calculation Of Fragment Size For Surface Energy and Strain R...mentioning

confidence: 99%

Energy Partitioning, Dynamic Fragmentation, and Off‐Fault Damage in the Earthquake Source Volume

et al. 2021

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“…The existence of a discrete hierarchy of scales has in addition been suggested by Sornette and Sammis [1995] based on the analysis of accelerated seismicity prior to large earthquakes and recently by Pisarenko et al [2004] by using a non-parametric measure of deviations from power laws applied to the magnitude-frequency distributions of earthquakes in subduction zones. Evidence of a hierarchy of scales is also found in fragmentation and rupture processes [Sadovskii, 1999;Geilikman and Pisarenko, 1989;Sahimi and Arbabi, 1996;Ouillon et al, 1996;Johanson and Sornette, 1998;Suteanu, 2000].…”

Section: Introductionmentioning

confidence: 99%

Constraints on the size of the smallest triggering earthquake from the epidemic‐type aftershock sequence model, Båth's law, and observed aftershock sequences

Sornette

Werner

2005

J. Geophys. Res.

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[1] The physics of earthquake triggering together with simple assumptions of selfsimilarity imply the existence of a minimum magnitude m 0 below which earthquakes do not trigger other earthquakes. Noting that the magnitude m d of completeness of a seismic catalog is not, in general, the same as the magnitude m 0 of the smallest triggering earthquake, we compare observed aftershock sequence parameters with the predictions made by the epidemic-type aftershock sequence model to constrain the value of m 0 . In particular, we use quantitative fits to observed aftershock sequences from three previous studies, as well as Båth's law, to obtain four estimates of m 0 . We show that the branching ratio n (average number of triggered earthquakes per earthquake, also equal to the fraction of aftershocks in a seismic catalog) is the key parameter controlling the estimate of the minimum triggering magnitude m 0 . Conversely, physical upper bounds for m 0 estimated from rate and state friction indicate that at the very least, 55% of all earthquakes are aftershocks.Citation: Sornette, D., and M. J. Werner (2005), Constraints on the size of the smallest triggering earthquake from the epidemic-type aftershock sequence model, Båth's law, and observed aftershock sequences,

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“…The upper and lower fractal cutoff scales appear to be related to the shearing displacement and the mineral constitution [ Weiss and Gay , 1998]. Power law exponents, i.e., fractal dimensions, observed for natural fragmented objects range from 1.4 to 3 [ Turcotte , 1992] depending on the rock type and on the fragmentation process [ Blenkinsop and Fernandes , 2000; Suteanu et al , 2000; Hecht , 2000].…”

Section: Introductionmentioning

confidence: 99%

Fracture roughness and gouge distribution of a granite shear band

Amitrano

Schmittbuhl

2002

J. Geophys. Res.

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[1] Localization of deformation during fracture mechanical tests leads to the development of shear bands. We performed triaxial tests using Sidobre granite at four different confining pressures (from 20 to 80 MPa). We compared two sets of tests: one set was stopped immediately after the formation of the shear band; a second one included additional shear deformation. From the analysis of thin sections of these laboratory samples, we characterize the typical microstructures in the shear band (mode I and II cracks, Riedel cracks, cataclastic flow). Statistical properties of rupture surface roughness and gouge grain size reveals scaling invariance. Using a mechanical profiler, the fracture roughness is measured along parallel profiles and shown to be correctly described over up to 3 orders of magnitude by self-affine geometry with a roughness exponent close to z = 0.80. This property is very similar to tensile crack even if local processes are different. The influence of the slip is observed. Fracture surfaces are rougher along the slip direction (z = 0.74) than perpendicular to it (z* = 0.80). The confining pressure is shown to have a weak effect on the fracture roughness. It smoothes the surface: slight increase of the roughness exponent. Gouge particles extracted from the shear band present a power law distribution with an exponent ranging from 1.44 to 1.91. This exponent appears to increase with the shearing displacement and the confining pressure. When a significant shear of the band is combined with a high confining pressure (i.e., impeded dilation of the band), the hallmark of fragmentation is observed for the particle distribution and related to a smoothing of the band boundary.

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Fractal Approach of Structuring by Fragmentation

Cited by 4 publications

References 16 publications

Energy Partitioning, Dynamic Fragmentation, and Off‐Fault Damage in the Earthquake Source Volume

Energy Partitioning, Dynamic Fragmentation, and Off‐Fault Damage in the Earthquake Source Volume

Constraints on the size of the smallest triggering earthquake from the epidemic‐type aftershock sequence model, Båth's law, and observed aftershock sequences

Fracture roughness and gouge distribution of a granite shear band

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